How to write mathematical ODE equation of PI controller, with saturation and rate limiter in differential equation form?

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I want to write a mathematical ODE equation of PI controller, with saturation and rate limiter in differential equation form. I can write PI controller, but how to incorporate it with saturation and rate limiter?

du/dt = Wt_rated - wt; 
B_ref = Kp *(Wt_rated - wt) + Ki *u

Please see the attached photograph. PI Controller with saturation and rate limiter.